Bank exam Archives - Page 8 of 9

Shortcut to divide 2 digit by 9

December 29, 2018October 9, 2013 by Bank Exams

Shortcut to divide any 2 digit number by 9

Dividing a two digit number by 9 using the method taught to us in our school days may take a minute. However, by applying the shortcut to divide 2 digit by 9 you can mentally calculate the answer within seconds.

Shortcut to divide 2 digit by 9 steps

Let us see the steps now

Step 1: Enter the ten’s digit of the number as it is.

Step 2: To get the unit’s place digit add the ten’s place digit number and Unit’s place digit number and put the decimal point after the ten’s place digit.

Examples

Let us consider an example

Example 1:23÷ 9=?

Step 1: We enter the ten’s place digit as it is

Ten’s place digit=2

Step 2: We get the unit’s place digit by adding ten’s place digit and unit’s place digit

2+3=5

Unit’s place digit=5

Now add a decimal point between the unit’s place digit and the ten’s place digit to arrive at the answer

Ans 23÷ 9 =2.5

Example 2: 32÷ 9=?

Step 1: We enter the ten’s place digit as it is

Ten’s place digit=3

Step 2: We get the unit’s place digit by adding ten’s place digit and unit’s place digit

3+2=5

Unit’s place digit=5

Now add a decimal point between the unit’s place digit and the ten’s place digit to arrive at the answer

Ans 32÷ 9 =3.5

Example 3: 47÷ 9=?

Step 1: We enter the ten’s place digit as it is

Ten’s place digit=4

Step 2: We get the unit’s place digit by adding ten’s place digit and unit’s place digit

4+7=11.

Since it is a 2 digit number, add both numbers that is 1 + 1 to get unit’s place digit. We get, unit place digit=1+1=2

Also carry forward the ten’s place digit to step 1

Step 3: Add carry forward(1) from step 2 to original ten’s place digit of given number. we get, ten’s place digit= 4 + 1=5

Now add a decimal point between the unit’s place digit and the ten’s place digit to arrive at the answer

Ans 47÷ 9 =5.2

Shortcut to multiply any 2 digit number by 11

December 17, 2018October 4, 2013 by Bank Exams

Multiplying any 2 digit number by 11 is the easiest when you know this trick. Shortcut to multiply 2 digit by 11 is very easy to mentally get the correct answer. It saves a lot of time when this is part of a bigger problem given in bank exams.

Shortcut to multiply 2 digit by 11

Let us now quickly go through the steps

Step 1: Enter the unit’s place digit as it is. This is the last digit of your answer.

Step 2: Enter the ten’s place digit leaving a blank in between for the middle digit.

Step 3: To find the middle digit, add unit’s place digit and ten’s place digit and input the digit in the blank.

NOTE: On adding if you arrive at a 2 digit number then, input only the unit’s place of the middle digit in the blank and add the ten’s place digit of the middle digit to the original ten’s place digit of the number.

Let me explain with an example to make it easy to understand

Example 1: 42 X 11

Step 1: Here the unit’s place digit is 2, enter as it is i.e 2

Step 2: Here the ten’s place digit is 4, so input it as follows leaving a blank between the unit’s place digit and the ten’s place digit for the middle digit.

4_2

Step 3: Now, By adding unit’s place digit and ten’s place digit (4+2=6)we get the middle digit as 6 which we enter in the blank as follows.

462

Ans : 42 x 11=462

Example 2: 31 X 11

Step 1: Here the unit’s place digit is 1, enter as it is i.e 1

Step 2: Here the ten’s place digit is 3, so input it as follows leaving a blank between the unit’s place digit and the ten’s place digit for the middle digit.

3_1

Step 3: Now, By adding unit’s place digit and ten’s place digit (3+1=4)we get the middle digit as 4 which we enter in the blank as follows.

341

Ans : 31 x 11=341

Example 3: 53 X 11

Step 1: Here the unit’s place digit is 3, enter as it is i.e 3

Step 2: Here the ten’s place digit is 5, input it as follows leaving a blank between the unit’s place digit and the ten’s place digit for the middle digit.

5_3

Step 3: Now, By adding unit’s place digit and ten’s place digit (3+5=8)we get the middle digit as 8 which we enter in the blank as follows.

583

Ans : 53 x 11=583

Example 4: 67 X 11

Step 1: Here the unit’s place digit is 7, enter as it is i.e 7

Step 2: Here the ten’s place digit is 6, so input it as follows leaving a blank between the unit’s place digit and the ten’s place digit for the middle digit.

6_7

Step 3: Now, By adding unit’s place digit and ten’s place digit (7+6=13)we get

2 digit number then, input only the unit’s place of the middle digit(3) in the blank and carry forward the ten’s place digit to step 4.

637

Step 4: Add the ten’s place digit(1) to the original ten’s place digit(6) of the number as follows.

6+1=7

Ans : 67 x 11=737

Example 5: 49 X 11

Step 1: Here the unit’s place digit is 9, enter as it is i.e 9

Step 2: Here the ten’s place digit is 4, so input it as follows leaving a blank between the unit’s place digit and the ten’s place digit for the middle digit.

4_9

Step 3: Now, By adding unit’s place digit and ten’s place digit (9+4=13)we get

2 digit number then, input only the unit’s place of the middle digit(3) in the blank and carry forward the ten’s place digit to step 4.

439

Step 4: Add the ten’s place digit(1) to the original ten’s place digit(4) of the number as follows.

4+1=5

Ans : 49 x 11=539

Tip to remember: Ten’s place (ten’s place + unit place) Unit’s place

How to verify if a number is perfect cube

December 23, 2018September 30, 2013 by Bank Exams

Learn how to verify if a number is perfect cube using Prime Factorization Method. It is the method to use to find out if a given number is a perfect cube or not if you want accurate results. Before going into the details of the Prime Factorization Method, it is helpful to know what Prime factors are.

Prime numbers are those numbers which are divisible only by 1 and the number itself. These numbers do not have any other divisible factors.

Prime numbers such as 2, 3, 5, 7, 11, 13, 17, 19, 23, 29……. are also known as the prime factors.

Now, we shall see how Prime Factorization Method is done from the below steps.

Step 1: Find the prime factors of the given number.

Step 2:Group the factors in 3’s of equal factors.

Step 3:After grouping,

If you are not left with any separate single or double factor, then the given number is a perfect cube.

If you are left with any separate single or double factor, then the given number is not a perfect cube.

Let us consider some examples to understand the Prime Factorization Method better.

Examples

Example of a number which is a perfect cube.

Example1:Verify if 216 is a perfect cube.

Step1:We start by finding prime factors of 216.

Prime factors of 216 are 2x2x2x3x3x3

Step 2: Grouping the factors into 3’s

(2x2x2) x (3x3x3)

Step 3: After grouping, we notice that no factor is left.

Therefore we can say that 216 is definitely a perfect cube.

Example of a number which is not a perfect cube.

Example 2:Verify if 1024 is a perfect cube

Step1:We start by finding prime factors of 1024.

Prime factors of 1024 are 2x2x2x2x2x2x2x2x2x2

Step 2:Grouping the factors into 3’s

(2x2x2) x (2x2x2) x (2x2x2) x 2

Step 3: After grouping, we notice that factor 2 is left.

Therefore we can say that 1024 is not a perfect cube.

Shortcut to find cube of any number from 1 to 100

December 28, 2018September 20, 2013 by Bank Exams

Finding cube of a number above 20 in the usual way is difficult and time consuming. With this Shortcut to find cube of any number, you can easily calculate cube of a number within seconds.

Short cut to find cube of number steps

Step 1: Assume the ten’s place number of the given number as a and the unit’s place number as b.
Step 2: Now, we all know that (a+b)³=a³ + 3a²b + 3ab² + b³

We shall manipulate the same formula to calculate the cube of a number.

(i)Find b³ to get the last digit

If you get two digit number then, add ten’s place digit to 3ab²

(ii) Find 3ab²

If you get two digit number then, keep the unit’s place digit and and
add ten’s place digit to 3a²b.

(iii) Find 3a²b
If you get two digit number then, keep the unit’s place digit and and
add ten’s place digit to a³.

(iv) Find a³

If you get two digit number then, just add the carried forward digit if any

and write the number.

Cube of any 2 digit number will be in the pattern of
a³ 3a²b 3ab² b³

Cube To make things easier it is good to memorize the cubes of numbers from

1 to 10
13=1
23=8
33=27
43=64
53=125
63=216
73=343
83=512
93=729

Examples

Lets use this method to calculate the cube of a number with help of an example to understand better

Example 1: 32³=?
Step 1: Assume a= 3 and b= 2
Step 2: Now substituting the values of a and b in the below pattern
a³ 3a²b 3ab² b³

(i) Finding b³ Now that is
b³=2³=8
We get the last digit as 8.

(ii) Finding 3ab²
3ab²=3(3)(2)²=36
From this we will keep the one’s place digit(6) and add the ten’s place digit(3) to 3a²b.

(iii)Finding 3a²b and adding ten’s place digit(3)
3a²b=3(3)²(2)=3(9)(2)=54 + 3= 57

From this we will keep the one’s place digit(7) and add ten’s place digit(5) to b in the next step.

(iv) Finding a³ and adding the ten’s place digit(5) from previous step
a³=3³=27+5=32
From this we get the number as 32

From all the above steps we get

Ans 32³=32768

Example 2: 47³=?
Step 1: Assume a= 4 and b= 7
Step 2: Now substituting the values of a and b in the below pattern
a³ 3a²b 3ab² b³

(i) Finding b³ Now that is
b³=73=343
We get the last digit as 3.

(ii) Finding 3ab²
3ab²=3(4)(7)²=12 x 49=588 (Tip: Use Shortcut to multiply any 2 digit by 2 digit)
Now add 34 that you got from step 1 to 588,we get 588+34=622
From this we will keep the one’s place digit(2) and add remaining digits(62) to 3ab².

(iii)Finding 3a²b and adding remaining digits of step 2(62)
3a²b=3(4)²(7)=16 x 21=336
336+ 62=398
From this we will keep the one’s place digit(8) and add remaining digits(39) to a³.

(iv) Finding a³ and adding the remaining digits from step 3
a³=4³=64
64 + 39=103

From all the above steps we get
47³=103823

With practice you will be able to find the cube of any two digit
number within seconds.

Try it with other numbers and let us know if it was helpful to you!

If you have any other shortcut way of finding the cube of a number,
feel free to share it here.

Shortcut to Multiply 2 digit by 2 digit

November 22, 2020October 23, 2011 by Bank Exams

You can always use the method that we are used to in our school days to multiply any two numbers if you have sufficient time. However, bank exams is all about answering maximum number of questions accurately in limited time. How efficiently you manage time depends on how well you can apply the shortcut tricks that you learnt and practiced.

Multiply 2 digit by 2 digit shortcut method

Here is a shortcut to multiply any 2 digit number by a 2 digit number within seconds.

Let us see the steps to multiply a 2 digit number by a 2 digit number

Step 1:Multiply the ten’s place digit of the 1st number with ten’s place digit of the 2nd number to get the ten’s place digit of your answer.

Step 2:Leave a blank space in between.Now multiply the unit’s place digit of the 1st number with the unit’s place digit of the 2nd number to get the unit’s place digit of your answer.

Step 3:Find the product of the inside numbers and the product of the extremes and add both and insert the digit in the blank space.

Let us consider an example to understand better

Example 1: 41 x 31=?

Step 1:Multiply ten’s place digit of both the numbers as shown below

41 x 31=12 (i.e 4 x 3)

Step 2: Leave a blank space in between the ten’s place digit and unit place digit. 12_

Multiply unit’s place digit of both the numbers as shown below

41 x 31=1(i.e 1 x 1)

we get, 12_1

Step 3: Find the product of inside numbers(1 x 3=3)

Find the product of extremes (4 x 1=4)

41 x 31

Now adding the product of inside numbers and extremes

we get,

(1 x 3)+(4 x 1)=3+4=7

The middle digit is 7

Ans: 41 x 31=1271

Example 2: 46 x 36=?

Step 1: Multiply ten’s place digit of both the numbers as shown below

46 x 36=12(i.e 4 x 3)

Step 2: Leave a blank space in between the ten’s place digit and unit place digit as below.

12_

Multiply unit’s place digit of both the numbers as shown below to get the unit’s place digit which is 6

46 x 36=36 (i.e 6 x 6)

12_6

Here we are getting 2 digit number on multiplication, we will keep the unit’s place digit(6) and carry forward ten’s place digit(3) to step 3 as shown below

Step 3:Find the product of inside numbers(6 x 3=18)

Find the product of extremes (4 x 6=24)

46 x 36

Now adding the product of inside numbers and extremes

we get,18+24=42

Now we shall add the carry forward ten’s place digit(3) we got from step 2.

42+3=45

We shall keep unit’s place digit(5) and carry forward ten’s place digit(4) to step 1.

1256. Middle number is 5.

Step 4:Adding carry forward(4) from step 3 to step 1 answer, we get

12+4=16

Ans: 46 x 36=1656

Example 3: 32 x 34=?

Step 1: Multiply ten’s place digit of both the numbers as shown below

32 x 34=9(i.e 3 x 3)

Step 2: Leave a blank space in between the ten’s place digit and unit place digit as below.

Multiply unit’s place digit of both the numbers as shown below to get the unit’s place digit which is 6

32 x 34=8 (i.e 4 x 2)

9_8

Step 3:Find the product of inside numbers(2 x 3=6)

Find the product of extremes (3 x 4=12)

32 x 34

Now adding the product of inside numbers and extremes

we get,6+12=18

We shall keep unit’s place digit(8) and carry forward ten’s place digit(1) to step 1.

988. Middle number is 8.

Step 4:Adding carry forward(1) from step 3 to step 1 answer, we get

9+1=10

Ans 32 X 34= 1088

Tip to remember this trick: Always keep in mind that whenever you get a 2 digit number on multiplication, the ten’s place digit is always carried forward to the number immediately to the left direction of it.

Also Read
Shortcut to divide any 2 digit number by 5
Vedic math trick to check multiplication
3 digit multiplication trick in banking